Mane was taken off with a minute remaining in Senegal's 2-0 World Cup qualifying win over Cape Verde Islands on Saturday.
Liverpool said the injury "could keep him out of action for up to six weeks" starting with Saturday's league game against arch-rivals Manchester United at Anfield.
Mane has scored three goals in five Premier League appearances this season and has just returned from a three-match suspension.
The speedy forward picked up a red card during the 5-0 loss to Manchester City last month but was back in the starting line-up for the 1-1 draw at Newcastle before the international break.
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(Reporting by Simon Evans, editing by Ed Osmond)
